Co-Optimizing Distributed Energy Resources in Linear Complexity under Net Energy Metering

TL;DR

This work tackles the challenge of co-optimizing behind-the-meter DERs—renewables, storage, and flexible loads—under net energy metering X tariffs within a scalable framework. It introduces a linear-complexity Myopic Co-Optimization (MCO) that relaxes storage constraints and yields closed-form, threshold-based schedules that depend only on realized renewable output $g_t$, not on the full stochastic model. A sufficient-optimality condition shows when MCO matches the stochastic DP, revealing a three-zone (net consumption, net production, net-zero) structure and complementarity properties that expand the net-zero operational window to reduce reverse power flows. Numerical results demonstrate orders-of-magnitude reductions in computation compared to MPC, with small optimality gaps and clear prosumer and DSO benefits, including improved resilience and reduced grid congestion. Overall, the approach offers a practical, decentralized EMS paradigm for large-scale DER integration under NEM tariffs.

Abstract

The co-optimization of behind-the-meter distributed energy resources is considered for prosumers under the net energy metering tariff. The distributed energy resources considered include renewable generations, flexible demands, and battery energy storage systems. An energy management system co-optimizes the consumptions and battery storage based on locally available stochastic renewables by solving a stochastic dynamic program that maximizes the expected operation surplus. To circumvent the exponential complexity of the dynamic program solution, we propose a closed-form and linear computation complexity co-optimization algorithm based on a relaxation-projection approach to a constrained stochastic dynamic program. Sufficient conditions for optimality for the proposed solution are obtained. Numerical studies demonstrate orders of magnitude reduction of computation costs and significantly reduced optimality gap.

Figures (8)

• Figure 1: Net energy metering scheme, with $d, g \in \mathbb{R}_+$ being the variables of consumption and renewable DG, respectively, whereas $e, z \in \mathbb{R}_+$ are the variables of storage output and net consumption, respectively. Arrows of variables correspond to the positive direction.
• Figure 2: Optimal prosumer decisions under the myopic co-optimization: optimal net consumption $z^\dagger_t$ (red), optimal total consumption $d^\dagger_t$ (black), optimal storage operation $e^\dagger_t$ (blue), and optimal DG-adjusted total consumption $\tilde{d}^\dagger_t:= d_t^\dagger - g_t$ (green), assuming that $\Delta_t^{+}\ge \overline{e}^\dagger_t$ and $\underline{e}^\dagger_t=\overline{e}^\dagger_t$.
• Figure 3: Optimal prosumer decisions under special case in Sec. \ref{['subsec:Insights']} with decision thresholds: $\Delta^+_t=\max\{f_t(\pi^+_t)-\underline{e},0\}, \sigma^+_t=\max\{f_t(\gamma)-\underline{e},0\}, \sigma^-_t=f_t(\gamma)+\overline{e}, \\ \Delta^-_t=f_t(\pi^-_t)+\overline{e}$, and assuming $\Delta^+_t \ge \overline{e}$ and $\underline{e}=\overline{e}$.
• Figure 4: Solution gap of MCO and MPC algorithms under different renewable levels. The two vertical lines represent the $C-8$ and $C-4$ storage charging/discharging levels.
• Figure 5: Net consumption distribution ($\overline{e}=\underline{e}=1$ (kW)).

Theorems & Definitions (18)

• Theorem 1: Myopic co-optimization optimal scheduling
• proof
• Corollary 1
• proof
• Theorem 2: Sufficient optimality condition
• proof
• Corollary 2
• proof
• Theorem 3: Prosumer consumption decision under NEM X
• Lemma 1: Marginal value of storage